Question 1063274
For this problem we use the normal probability(P) distribution and its associated z-values to determine probabilities
:
z-value = (X - mean) / standard deviation
:
(a) P ( X > 5000 ) = 1 - P ( X < 5000 )
z-value = ( 5000 - 5000 ) / 1000 = 0
P ( X > 5000 ) = 1 - 0.50 = 0.50
:
(b) P ( 5000 < X < 6000 ) = P ( X < 6000 ) - P ( X < 5000 )
z-value = ( 6000 - 5000 ) / 1000 = 1
P ( 5000 < X < 6000 ) = 0.8413 - 0.5000 = 0.3413
:
(c) P ( X > 7000 ) = 1 - P ( X < 7000 )
z-value = ( 7000 - 5000 ) / 1000 = 2
P ( X > 7000 ) = 1 - 0.9772 = 0.0228
: